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Napier's bones for children

Show how rods can help organise multiplication facts and partial products.

Quick answer

Napier's bones are a clever way to multiply big numbers using rods that show multiplication facts. You can use them to break down hard multiplication into easier steps, just like using arrays or repeated addition.

Learning outcome

By the end of this page, you will be able to use Napier's bones to multiply a number by a single digit, and understand how they help you see multiplication in a new way. Success signs:
  • You can line up the rods and read the multiplication facts from them
  • You can add up the partial products to find the final answer
  • You can explain how Napier's bones make multiplication easier
  • You can use the rods to multiply numbers like 4 × 7 or 8 × 9

Why this matters

Multiplication can be tricky, especially when you're multiplying bigger numbers. Napier's bones were invented in the 1600s by a Scottish mathematician named John Napier to help people multiply faster and more accurately. These rods are like a magic tool that helps you see how multiplication works in a visual way. Even today, you can use them to understand how multiplication works, and they’re a great way to practice your times tables.

How it works

Napier's bones are made of little rods, each with a multiplication table on it. You line them up like building blocks to multiply a number by a single digit. Here's how:
  1. Choose your rods: For a number like 432, you need rods for 4, 3, and 2.
  2. Line up the rods: Put them side by side, with the 4 rod on the left, 3 in the middle, and 2 on the right.
  3. Choose your multiplier: If you're multiplying by 7, look at the 7th row on each rod.
  4. Read the numbers: Each rod shows a partial product. Read the numbers in the row from left to right.
  5. Add them up: Add the partial products together to get your final answer.

Examples you can see

Let’s try multiplying 432 by 7 using Napier's bones. Step 1: Get your rods for 4, 3, and 2. Step 2: Line them up like this:
4 3 2
0 4 8 0 3 6 0 2 4
Step 3: Look at the 7th row:
4 3 2
2 8 5 6 2 1 4 2 1 4 2 8
Step 4: Read the partial products from left to right:
  • First number: 2
  • Second number: 8
  • Third number: 5
  • Fourth number: 6
Step 5: Add them up:
  • 2 + 8 = 10
  • 10 + 5 = 15
  • 15 + 6 = 21
So, 432 × 7 = 3024.

Try it as a mini adventure

Imagine you're a treasure hunter, and you’ve found a chest with a special lock. The lock only opens if you can multiply 567 by 8 using Napier's bones. You need to find the right rods, line them up, and read the answer to unlock the treasure.
  1. Find your rods: You need the rods for 5, 6, and 7.
  2. Line them up: Put them in order: 5, 6, 7.
  3. Choose the row: Look at the 8th row on each rod.
  4. Read the numbers: From left to right, what do you see?
  5. Add them up: What is your final answer?
Can you solve the treasure lock?

Common mistakes

  • Mistake: Reading the wrong row from the rods. Why it happens: You might accidentally look at the 6th row instead of the 8th. Fix: Double-check the row number and count carefully.
  • Mistake: Adding the numbers wrong. Why it happens: You might add 5 + 6 = 11, but forget to carry the 1. Fix: Write down your addition step by step, and remember to carry when needed.
  • Mistake: Mixing up which rod is for which digit. Why it happens: You might put the 7 rod where the 4 rod should be. Fix: Match each digit to its rod and check your order.

Parent and carer guide

Parents and carers can help by:
  • Letting the child choose the rods and line them up themselves
  • Practicing with simple numbers first, like 123 × 4
  • Encouraging the child to read the numbers aloud and explain what they see
  • Using the rods to make multiplication fun and visual
  • Not worrying if the child makes mistakes – they're learning!
You can also make your own Napier's bones using paper and pencil. Draw a grid and write the multiplication table on each rod. This helps children understand how the rods work.

Practice questions

  1. Use Napier's bones to multiply 245 by 3.
  2. What is 678 × 6?
  3. Try 129 × 5.
  4. What is 341 × 9?
  5. Use the rods to find 789 × 4.
Answers:
  1. 735
  2. 4068
  3. 645
  4. 3069
  5. 3156

FAQ

What are Napier's bones?

Napier's bones are rods that help you multiply numbers. Each rod shows a multiplication table, and you can line them up to find the answer to a multiplication problem.

Who invented Napier's bones?

John Napier, a Scottish mathematician, invented them in the 1600s. He also invented logarithms, which are another way to make math easier.

Can I use Napier's bones for any multiplication?

Yes! You can use them to multiply any number by a single digit, like 342 × 5 or 761 × 8.

Are Napier's bones still useful today?

They’re not used much in everyday life anymore, but they’re great for learning how multiplication works and for practicing times tables.

How can I make my own Napier's bones?

You can draw rods on paper, with each rod showing a multiplication table. For example, the rod for 4 would show 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.